Background: Individuals with underlying chronic illnesses have demonstrated considerable hesitancy towards COVID-19 vaccines. These concerns are primarily attributed to their concerns over the safety profile. Real-world data on the safety profile among COVID-19 vaccinees with comorbid conditions are scarce. This study aimed to ascertain the side-effects profile after two doses of COVID-19 vaccines among chronic-disease patients. Methodology: A cross-sectional questionnaire-based study was conducted among faculty members with comorbid conditions at a public educational institute in Saudi Arabia. A 20-item questionnaire recorded the demographics and side effects after the two doses of COVID-19 vaccines. The frequency of side effects was recorded following each dose of vaccine, and the association of the side-effects score with the demographics was ascertained through appropriate statistics. Results: A total of 204 patients with at least one comorbid condition were included in this study. A total of 24 side effects were reported after the first dose and 22 after second dose of the COVID-19 vaccine. The incidence of at least one side effect was 88.7% and 95.1% after the first and second doses of the vaccine, respectively. The frequent side effects after the first dose were pain at the injection site (63.2%), fatigue (58.8%), fever (47.5%), muscle and joint pain (38.7%), and headache (36.3%). However, pain at the injection site (71.1%), muscle and joint pain (62.7%), headache (49.5%), fever (45.6%), and stress (33.3%) were frequent after the second dose. The average side-effects score was 4.41 ± 4.18 (median: 3, IQR: 1, 6) and 4.79 ± 3.54 (median 4, IQR: 2, 6) after the first and second dose, respectively. Female gender, diabetes mellitus, hypertension, hyperlipidemia, comorbidity > 2, family history of COVID-19, and the AstraZeneca vaccine were significantly associated with higher side-effect scores. Only 35.8% of study participants were satisfied with the safety of COVID-19 vaccines. Conclusions: Our analysis showed a high proportion of transient and short-lived side effects of Pfizer and AstraZeneca vaccines among individuals with chronic illnesses. However, the side-effects profile was comparable with the safety reports of phase 3 clinical trials of these vaccines. The frequency of side effects was found to be associated with certain demographics, necessitating the need for further investigations to establish a causal relationship. The current study’s findings will help instill confidence in the COVID-19 vaccines among people living with chronic conditions, overcome vaccine hesitancy, and increase vaccine coverage in this population.